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We describe the process of using ArtiSynth, a 3D biomechanical simulation platform, to build models of the vocal tract and upper airway which are capable of simulating speech sounds. ArtiSynth allows mass-spring, finite element, and rigid body models of anatomical components (such as the face, jaw, tongue, and pharyngeal wall) to be connected to various acoustical models (including source filter and airflow models) to create an integrated model capable of sound production. The system is implemented in Java, and provides a class API for model creation, along with a graphical interface that permits the editing of models and their properties. Dynamical simulation can be interactively controlled through a 'timeline' interface that allows online adjustment of model inputs and logging of selected model outputs. ArtiSynth's modeling capabilities, in combination with its interactive interface, allow for new ways to explore the complexities of articulatory speech synthesis, chewing and swallowing and dysfunction of the upper airway.